Implements the shape functions of a triangular (2D) element. Shape. More...

#include <pzshapetriang.h>

Inheritance diagram for pzshape::TPZShapeTriang:

Collaboration diagram for pzshape::TPZShapeTriang:

Static Public Member Functions
static void	Shape (TPZVec< REAL > &pt, TPZVec< int64_t > &id, TPZVec< int > &order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the values of the shape functions and their derivatives for a triangular element. More...

static void	SideShape (int side, TPZVec< REAL > &pt, TPZVec< int64_t > &id, TPZVec< int > &order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)

static void	ShapeOrder (TPZVec< int64_t > &id, TPZVec< int > &order, TPZGenMatrix< int > &shapeorders)
	returns the polynomial order in the natural ksi, eta of the side associated with each shapefunction More...

static void	SideShapeOrder (int side, TPZVec< int64_t > &id, int order, TPZGenMatrix< int > &shapeorders)
	returns the polynomial order in the natural ksi, eta of the internal shapefunctions of a side More...

static void	ShapeCorner (TPZVec< REAL > &pt, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the corner shape functions for a triangular element. More...

static void	ShapeGenerating (TPZVec< REAL > &pt, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the generating shape functions for a quadrilateral element. More...

static void	ShapeInternal (TPZVec< REAL > &x, int order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi, int triangle_transformation_index)
	Compute the internal functions of the triangle shape function at a point. More...

static void	ShapeInternal (TPZVec< REAL > &x, int order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)

static void	ProjectPoint2dTriangToRib (int rib, TPZVec< REAL > &in, REAL &out)
	Projects a point from the interior of the element to a rib. More...

static void	TransformDerivativeFromRibToTriang (int rib, int num, TPZFMatrix< REAL > &dphi)
	Transforms the derivative of a shapefunction computed on the rib into the two dimensional derivative of the function with respect to the element. The parameter dphi should be dimensioned (2,num), at least. More...

static int	GetTransformId2dT (TPZVec< int64_t > &id)
	Method which identifies the triangular transformation based on the IDs of the corner nodes. More...

static void	TransformPoint2dT (int transid, TPZVec< REAL > &in, TPZVec< REAL > &out)
	Transform the coordinates of the point in the space of the triangle master element based on the transformation id. More...

static void	TransformDerivative2dT (int transid, int num, TPZFMatrix< REAL > &in)
	Transform the derivatives of num shapefunctions in place for a triangle. More...

static int	NConnectShapeF (int side, int order)
	Number of shapefunctions of the connect associated with the side, considering the order of interpolation of the element. More...

static int	NShapeF (TPZVec< int > &order)
	Total number of shapefunctions, considering the order of interpolation of the element. More...

static TPZTransform< REAL >	ParametricTransform (int trans_id)

static void	ShapeInternal (int side, TPZVec< REAL > &x, int order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)

Static Public Member Functions inherited from pztopology::TPZTriangle
static void	GetSideHDivPermutation (int transformationid, TPZVec< int > &permgather)
	Identifies the permutation of the nodes needed to make neighbouring elements compatible in terms of order of shape functions. More...

static constexpr REAL	RefElVolume ()
	Volume of the master element (measure) More...

static void	GetSideHDivDirections (TPZVec< int > &sides, TPZVec< int > &dir, TPZVec< int > &bilinearounao)

static void	GetSideHDivDirections (TPZVec< int > &sides, TPZVec< int > &dir, TPZVec< int > &bilinearounao, TPZVec< int > &sidevectors)

template<class TVar >
static void	ComputeHDivDirections (TPZFMatrix< TVar > &gradx, TPZFMatrix< TVar > &directions)
	Compute the directions of the HDiv vectors. More...

template<class TVar >
static void	ComputeHCurlDirections (TPZFMatrix< TVar > &gradx, TPZFMatrix< TVar > &directions, const TPZVec< int > &transformationIds)

template<class TVar >
static void	ComputeHCurlFaceDirections (TPZVec< TVar > &v1, TPZVec< TVar > &v2, int transformationId)

static int	NBilinearSides ()

static int	SideDimension (int side)
	Returns the dimension of the side. More...

static void	LowerDimensionSides (int side, TPZStack< int > &smallsides)
	Get all sides with lower dimension on side. More...

static void	LowerDimensionSides (int side, TPZStack< int > &smallsides, int DimTarget)
	Get all sides with lower dimension but equal to DimTarget on side. More...

static void	HigherDimensionSides (int side, TPZStack< int > &high)
	Returns all sides whose closure contains side. More...

static int	NSideNodes (int side)
	Returns the number of nodes (not connectivities) associated with a side. More...

static int	SideNodeLocId (int side, int node)
	Returns the local node number of the node "node" along side "side". More...

static int	NumSides ()
	Returns the number of connects of the element (7) More...

static int	NumSides (int dimension)
	Returns the number of connects for a set dimension. More...

static int	NContainedSides (int side)
	Returns the number of nodes (not connectivities) associated with a side. More...

static int	ContainedSideLocId (int side)
	Returns the local connect along side "side" especial for hdivspace. More...

static int	ContainedSideLocId (int side, int c)
	Returns the local connect number of the connect "c" along side "side". More...

static void	Shape (TPZVec< REAL > &loc, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Compute the shape being used to construct the x mapping from local parametric coordinates. More...

template<class T >
static void	TShape (const TPZVec< T > &loc, TPZFMatrix< T > &phi, TPZFMatrix< T > &dphi)
	Compute the shape being used to construct the x mapping from local parametric coordinates. More...

template<class T >
static void	BlendFactorForSide (const int &side, const TPZVec< T > &xi, T &blendFactor, TPZVec< T > &corrFactorDxi)

static void	CenterPoint (int side, TPZVec< REAL > &center)
	Returns the barycentric coordinates in the master element space of the original element. More...

static bool	IsInParametricDomain (const TPZVec< REAL > &pt, REAL tol=pztopology::gTolerance)
	Verifies if the parametric point pt is in the element parametric domain. More...

static void	RandomPoint (TPZVec< REAL > &pt)
	Generates a random point in the master domain. More...

template<class T >
static bool	CheckProjectionForSingularity (const int &side, const TPZVec< T > &xiInterior)

template<class T >
static void	MapToSide (int side, TPZVec< T > &InternalPar, TPZVec< T > &SidePar, TPZFMatrix< T > &JacToSide)

static void	ParametricDomainNodeCoord (int node, TPZVec< REAL > &nodeCoord)

static MElementType	Type ()
	Returns the type of the element as specified in file pzeltype.h. More...

static MElementType	Type (int side)
	Returns the type of the element as specified in file pzeltype.h. More...

static TPZTransform	SideToSideTransform (int sidefrom, int sideto)
	Returns the transformation which takes a point from the side sidefrom of the side sideto. More...

static TPZTransform	TransformSideToElement (int side)
	Returns the transformation which transform a point from the side to the interior of the element. More...

static TPZTransform	TransformElementToSide (int side)
	Returns the transformation which transform a point from the interior of the element to the side. More...

static int	GetTransformId (TPZVec< int64_t > &id)
	Method which identifies the transformation based on the IDs of the corner nodes. More...

static int	GetTransformId (int side, TPZVec< int64_t > &id)
	Method which identifies the transformation of a side based on the IDs of the corner nodes. More...

static void	GetHDivGatherPermute (int transformid, TPZVec< int > &permute)
	return the vector which permutes the connects according to the transformation id More...

static TPZIntPoints *	CreateSideIntegrationRule (int side, int order)
	Create an integration rule over side. More...

Static Public Member Functions inherited from TPZSavable
static std::set< TPZRestoreClassBase * > &	RestoreClassSet ()
	This static function guarantees that the gMap object is available when needed. More...

static std::map< int, TPZRestore_t > &	ClassIdMap ()
	This static function guarantees that the gMap object is available when needed. More...

static std::pair< std::string, uint64_t >	NeoPZVersion ()

static void	Register (TPZRestoreClassBase *restore)

static void	RegisterClassId (int classid, TPZRestore_t fun)

static TPZSavable *	CreateInstance (const int &classId)

Static Public Attributes
static REAL	gTrans2dT [6][2][2]
	Data structure which defines the triangle transformations. More...

static REAL	gVet2dT [6][2]
	Data structure which defines the triangle transformations. More...

static REAL	gRibTrans2dT1d [3][2]
	Data structure which defines the triangle transformations. More...

static REAL	gVet1dT [3]
	Data structure which defines the triangle transformations. More...

Static Public Attributes inherited from pztopology::TPZTriangle
static int	SideNodes [3][2]

static int	FaceNodes [1][3]

static REAL	gTrans2dT [6][2][2]

Additional Inherited Members
Public Types inherited from pztopology::TPZTriangle
enum	{ NSides, NCornerNodes, Dimension, NFaces, NPermutations }
	Enumerate for topological characteristics. More...

typedef TPZIntTriang	IntruleType
	Typedef to numerical integration rule. More...

typedef TPZGraphElT2dMapped	GraphElType
	Typedef to graphical element type. More...

Public Member Functions inherited from pztopology::TPZTriangle
int	ClassId () const override
	Define the class id associated with the class. More...

void	Read (TPZStream &buf, void *context) override
	read objects from the stream More...

void	Write (TPZStream &buf, int withclassid) const override
	Writes this object to the TPZStream buffer. Include the classid if withclassid = true. More...

	TPZTriangle ()
	Default constructor. More...

virtual	~TPZTriangle ()
	Default destructor. More...

Public Member Functions inherited from TPZSavable
	TPZSavable ()

virtual	~TPZSavable ()

virtual std::list< std::map< std::string, uint64_t > >	VersionHistory () const

virtual std::pair< std::string, uint64_t >	Version () const

virtual bool	Compare (TPZSavable *copy, bool override=false)
	Compares the object for identity with the object pointed to, eventually copy the object. More...

virtual bool	Compare (TPZSavable *copy, bool override=false) const
	Compares the object for identity with the object pointed to, eventually copy the object. More...

Public Member Functions inherited from TPZRegisterClassId
template<typename T >
	TPZRegisterClassId (int(T::*)() const)

	TPZRegisterClassId ()=default

Static Protected Attributes inherited from pztopology::TPZTriangle
static int	fPermutations [6][7]
	Valid permutations between nodes. More...

static REAL	fTangentVectors [12][2]

Detailed Description

Implements the shape functions of a triangular (2D) element. Shape.

The triangular shape functions are also used in 3D elements
The range of the master element is 0,1

Definition at line 23 of file pzshapetriang.h.

Member Function Documentation

◆ GetTransformId2dT()

int pzshape::TPZShapeTriang::GetTransformId2dT ( TPZVec< int64_t > & id )

static

Method which identifies the triangular transformation based on the IDs of the corner nodes.

Parameters

id	indexes of the corner nodes

Returns: index of the transformation of the point

Definition at line 382 of file pzshapetriang.cpp.

Referenced by SideIdf().

◆ NConnectShapeF()

int pzshape::TPZShapeTriang::NConnectShapeF	(	int	side,
		int	order
	)

static

Number of shapefunctions of the connect associated with the side, considering the order of interpolation of the element.

Parameters

side	associated side
order	vector of integers indicating the interpolation order of the element

Returns: number of shape functions

Definition at line 424 of file pzshapetriang.cpp.

References PZError.

◆ NShapeF()

int pzshape::TPZShapeTriang::NShapeF ( TPZVec< int > & order )

static

Total number of shapefunctions, considering the order of interpolation of the element.

Parameters

order vector of integers indicating the interpolation order of the element

Returns: number of shape functions

Definition at line 442 of file pzshapetriang.cpp.

References test::res.

◆ ParametricTransform()

TPZTransform< REAL > pzshape::TPZShapeTriang::ParametricTransform ( int trans_id )

static

Definition at line 361 of file pzshapetriang.cpp.

References TPZTransform< T >::Mult(), and TPZTransform< T >::Sum().

Referenced by GetSideTransform().

◆ ProjectPoint2dTriangToRib()

void pzshape::TPZShapeTriang::ProjectPoint2dTriangToRib	(	int	rib,
		TPZVec< REAL > &	in,
		REAL &	out
	)

static

Projects a point from the interior of the element to a rib.

Parameters

rib	rib index to which the point should be projected
in	coordinate of the point at the interior of the element
out	coordinate of the point on the rib

Definition at line 356 of file pzshapetriang.cpp.

◆ Shape()

void pzshape::TPZShapeTriang::Shape	(	TPZVec< REAL > &	pt,
		TPZVec< int64_t > &	id,
		TPZVec< int > &	order,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Computes the values of the shape functions and their derivatives for a triangular element.

Parameters

pt	(input) point where the shape functions are computed
id	(input) indexes of the corner points which determine the orientation of the shape functions
order	(input) order of the side connects different from the corner connects (4 connects in this case)
phi	(output) values of the shape functions
dphi	(output) values of the derivatives of the shapefunctions These values depend on the point, the order of interpolation and ids of the corner points The shapefunction computation uses the shape functions of the linear element for its implementation

Definition at line 84 of file pzshapetriang.cpp.

References pzshape::TPZShapeLinear::GetTransformId1d(), and pzshape::TPZShapeLinear::ShapeInternal().

◆ ShapeCorner()

void pzshape::TPZShapeTriang::ShapeCorner	(	TPZVec< REAL > &	pt,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Computes the corner shape functions for a triangular element.

Parameters

pt	(input) point where the shape function is computed
phi	(output) value of the (3) shape functions
dphi	(output) value of the derivatives of the (4) shape functions holding the derivatives in a column

Definition at line 35 of file pzshapetriang.cpp.

◆ ShapeGenerating()

void pzshape::TPZShapeTriang::ShapeGenerating	(	TPZVec< REAL > &	pt,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Computes the generating shape functions for a quadrilateral element.

Parameters

pt	(input) point where the shape function is computed
phi	(input/output) value of the (4) shape functions
dphi	(input/output) value of the derivatives of the (4) shape functions holding the derivatives in a column

Computes the generating shape functions for a quadrilateral element

Parameters

pt	(input) point where the shape function is computed
phi	(input/output) value of the (4) shape functions
dphi	(input/output) value of the derivatives of the (4) shape functions holding the derivatives in a column

Definition at line 54 of file pzshapetriang.cpp.

◆ ShapeInternal() [1/3]

void pzshape::TPZShapeTriang::ShapeInternal	(	TPZVec< REAL > &	x,
		int	order,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi,
		int	triangle_transformation_index
	)

static

Compute the internal functions of the triangle shape function at a point.

Parameters

x	coordinate of the point
order	maximum order of shape functions to be computed
phi	shapefunction values
dphi	values of the derivatives of the shape functions
triangle_transformation_index	determines the transformation applied to the internal shape functions. This parameter is computed by the GetTransformId2dT method

See also: GetTransformId2dQ The internal The shape functions classes functions are the shapefunctions before being multiplied by the corner The shape functions classes functions.
Shape2dTriangleInternal is basically a call to the orthogonal shapefunction with the transformation determined by the transformation index

Definition at line 286 of file pzshapetriang.cpp.

References TPZMatrix< TVar >::Cols(), PZError, TPZFMatrix< TVar >::Resize(), and TPZMatrix< TVar >::Rows().

Referenced by pzshape::TPZShapePiram::ShapeInternal(), pzshape::TPZShapePrism::ShapeInternal(), and pzshape::TPZShapeTetra::ShapeInternal().

◆ ShapeInternal() [2/3]

void pzshape::TPZShapeTriang::ShapeInternal	(	TPZVec< REAL > &	x,
		int	order,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Definition at line 251 of file pzshapetriang.cpp.

References TPZMatrix< TVar >::Cols(), PZError, TPZFMatrix< TVar >::Resize(), and TPZMatrix< TVar >::Rows().

◆ ShapeInternal() [3/3]

void pzshape::TPZShapeTriang::ShapeInternal	(	int	side,
		TPZVec< REAL > &	x,
		int	order,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Definition at line 325 of file pzshapetriang.cpp.

References DebugStop, and pzshape::TPZShapeLinear::ShapeInternal().

◆ ShapeOrder()

void pzshape::TPZShapeTriang::ShapeOrder	(	TPZVec< int64_t > &	id,
		TPZVec< int > &	order,
		TPZGenMatrix< int > &	shapeorders
	)

static

returns the polynomial order in the natural ksi, eta of the side associated with each shapefunction

Definition at line 159 of file pzshapetriang.cpp.

References TPZGenMatrix< TObj >::Cols(), DebugStop, and TPZGenMatrix< TObj >::Rows().

◆ SideShape()

void pzshape::TPZShapeTriang::SideShape	(	int	side,
		TPZVec< REAL > &	pt,
		TPZVec< int64_t > &	id,
		TPZVec< int > &	order,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Definition at line 146 of file pzshapetriang.cpp.

References PZError, and Shape().

◆ SideShapeOrder()

void pzshape::TPZShapeTriang::SideShapeOrder	(	int	side,
		TPZVec< int64_t > &	id,
		int	order,
		TPZGenMatrix< int > &	shapeorders
	)

static

returns the polynomial order in the natural ksi, eta of the internal shapefunctions of a side

Parameters

sides is a vector with copy of side as much as needed, it depends on the order

Definition at line 209 of file pzshapetriang.cpp.

References DebugStop, and TPZGenMatrix< TObj >::Rows().

◆ TransformDerivative2dT()

void pzshape::TPZShapeTriang::TransformDerivative2dT	(	int	transid,
		int	num,
		TPZFMatrix< REAL > &	in
	)

static

Transform the derivatives of num shapefunctions in place for a triangle.

Parameters

transid	identifier of the transformation of the triangle element as obtained by the GetTransformId2dT method
num	number of shapefunctions needed to transform
in	matrix containing the values of the derivatives of the shapefunctions as a row vector the values of the derivatives contained in this matrix are modified upon return

Definition at line 412 of file pzshapetriang.cpp.

◆ TransformDerivativeFromRibToTriang()

void pzshape::TPZShapeTriang::TransformDerivativeFromRibToTriang	(	int	rib,
		int	num,
		TPZFMatrix< REAL > &	dphi
	)

static

Transforms the derivative of a shapefunction computed on the rib into the two dimensional derivative
of the function with respect to the element. The parameter dphi should be dimensioned (2,num), at least.

Parameters

rib	rib index along which the shapefunction is defined
num	number of shapefunction derivatives which need to be transformed
dphi	values of the derivatives of the shapefunctions

Definition at line 373 of file pzshapetriang.cpp.

◆ TransformPoint2dT()

void pzshape::TPZShapeTriang::TransformPoint2dT	(	int	transid,
		TPZVec< REAL > &	in,
		TPZVec< REAL > &	out
	)

static

Transform the coordinates of the point in the space of the triangle master element based on the transformation id.

Parameters

transid	identifier of the transformation of the element as obtained by the GetTransformId2dT method
in	coordinates of the variational parameter
out	coordinates of the transformed parameter

Definition at line 406 of file pzshapetriang.cpp.

Member Data Documentation

◆ gRibTrans2dT1d

REAL pzshape::TPZShapeTriang::gRibTrans2dT1d

static

Data structure which defines the triangle transformations.

Definition at line 146 of file pzshapetriang.h.

◆ gTrans2dT

REAL pzshape::TPZShapeTriang::gTrans2dT

static

Data structure which defines the triangle transformations.

Transformation of the point within a triangular face

Definition at line 141 of file pzshapetriang.h.

Referenced by TPZGeoElSide::NeighbourSideTransform().

◆ gVet1dT

REAL pzshape::TPZShapeTriang::gVet1dT

static

Data structure which defines the triangle transformations.

Definition at line 148 of file pzshapetriang.h.

◆ gVet2dT

REAL pzshape::TPZShapeTriang::gVet2dT

static

Data structure which defines the triangle transformations.

Definition at line 144 of file pzshapetriang.h.

Referenced by TPZGeoElSide::NeighbourSideTransform().

The documentation for this class was generated from the following files:

Shape/pzshapetriang.h
Shape/pzshapetriang.cpp

Static Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ GetTransformId2dT()

◆ NConnectShapeF()

◆ NShapeF()

◆ ParametricTransform()

◆ ProjectPoint2dTriangToRib()

◆ Shape()

◆ ShapeCorner()

◆ ShapeGenerating()

◆ ShapeInternal() [1/3]

◆ ShapeInternal() [2/3]

◆ ShapeInternal() [3/3]

◆ ShapeOrder()

◆ SideShape()

◆ SideShapeOrder()

◆ TransformDerivative2dT()

◆ TransformDerivativeFromRibToTriang()

◆ TransformPoint2dT()

Member Data Documentation

◆ gRibTrans2dT1d

◆ gTrans2dT

◆ gVet1dT

◆ gVet2dT